Backbench MPs called for TV debates in the competition for the Labour leadership as the party's ruling body met today to instigate a formal contest after Gordon Brown's resignation.

The deputy leader, Harriet Harman, stepped in to become leader of the party with immediate effect but has ruled herself out of the race.

The departing cabinet ministers David Miliband, Ed Balls and Ed Miliband are poised to launch leadership campaigns, with the older Miliband brother, David, the odds-on favourite to win.

However, the odds on the health secretary, Andy Burnham, shortened from 16-1 to 8-1 after he became the first cabinet minister to suggest the Lib-Lab coalition talks should end. His statement, put in mild terms, was interpreted by some as a tentative dipping of his toe in the leadership race.

Burnham is seen as something of a weather vane in the Labour party, and has broad support in the grassroots. Supporters say he will have popular appeal outside the party as well.

Labour's national executive committee met via phone conference tonightand agreed to meet within the month to set out the code of conduct for candidates and a timetable for a leadership election that would involve a full ballot of members and union affiliates. There is pressure for a leader to be in place as soon as possible to help prepare for a possible second election this year.

Senior Labour figures said there was pressure for the leadership contest to happen as quickly as possibly, certainly before the summer recess. The membership ballot is costly, however, and Labour is short of funds after the election campaign, so it could be delayed until the autumn.

A source in the meeting said there had been moving tributes to Gordon Brown, with members reflecting on his legacy after 13 years in power.

Balls, a close colleague of Brown, has made no secret of his desire to stand, but his majority was slashed to 1,000 last week, making him vulnerable in the case of another election.

David Miliband is keen to launch a clear and unambiguous campaign to counter the indecisive impression he gave with his U-turn on a leadership challenge two years ago. Ed Miliband is increasingly popular within the parliamentary party and has strong union support, but his national profile is relatively low.

One backbencher called for the leadership candidates to take part in a televised debate. John Mann, one of the first MPs to call for Brown to resign this week, said it would put them "to the test".

"I think it would be extremely important that we have a TV leadership debate between the candidates," he said. "For better or for worse, that is one of the things a party leader is going to need to do in the future, and I think that it would open it out to the wider public, including the wider membership. And I think that is essential."

Other potential candidates being discussed are the work and pensions secretary, Yvette Cooper, the MP for Dagenham, Jon Cruddas, and the home secretary, Alan Johnson. Johnson said: "I am not ruling myself in, out, up, down, sideways or below. We are going to talk about that in due course."

Despite some already having campaign teams in place, potential candidates are wary of declaring too early and risking their campaigns burning out. One source close to the cabinet said: "I don't suppose it will be long before people start sticking their oars in. But everyone will be thinking of William Hague in 1997: go too early [in your career] and blow it. That will be at the front of some of the less likely candidates' minds."

Hague had agreed to run as Michael Howard's number two in the aftermath of that election but had a last-minute change of heart and ran for the leadership, a job he was widely thought to have been too inexperienced for.

Another source close to one of the possible contenders said: "Remember how David Davis was clear favourite at the start of the Tory contest in 2005?" Davis was thought to have lost his campaign after starting as the favourite after expectations were raised too high in the early months and the party received his speech coolly at the party conference weeks before the ballot.

The bookmaker William Hill puts David Miliband at 4-9, Johnson at 13-2, Burnham at 8-1, Ed Miliband at 11-1, Balls at 14-1, Alistair Darling at 14-1, Harman at 22-1, Cruddas at 25-1, Peter Mandelson at 33-1, and Jack Straw at 33-1.